Extrapolation Accelerated PRESB Method for Solving a Class of Block Two-by-Two Linear Systems

Abstract

We use extrapolation acceleration technique to speed up the preconditioned square block matrix splitting iteration method for two-by-two block linear systems. It is shown that for relaxation parameter $ω$ = 4/3, the convergence factor of the iteration method under consideration is 1/3. This yields the robustness and efficiency of the method. Numerical examples confirm the theoretical results and demonstrate the effectiveness of the approach developed.